Deformations of W-algebras associated to simple Lie algebras

Abstract

Deformed $\W$--algebra $\W_{q,t}(\g)$ associated to an arbitrary simple Lie algebra $\g$ is defined together with its free field realizations and the screening operators. Explicit formulas are given for generators of $\W_{q,t}(\g)$ when $\g$ is of classical type. These formulas exhibit a deep connection between $\W_{q,t}(\g)$ and the analytic Bethe Ansatz in integrable models associated to quantum affine algebras $U_q(\G)$ and $U_t(\GL)$. The scaling limit of $\W_{q,t}(\g)$ is closely related to affine Toda field theories.